How do you simplify #(a^2/b^3)/(b^5/a)#?

Question

Eva Adamson · Accepted Answer

See the solution process below:

First, use this rule for dividing fractions: #(color(red)(a)/color(blue)(b))/(color(green)(c)/color(purple)(d)) = (color(red)(a) xx color(purple)(d))/(color(blue)(b) xx color(green)(c))# #(color(red)(a^2)/color(blue)(b^3))/(color(green)(b^5)/color(purple)(a)) = (color(red)(a^2) xx color(purple)(a))/(color(blue)(b^3) xx color(green)(b^5))# Now, use these two rules of exponents to multiply the terms in the numerator and denominator: #a = a^color(red)(1)# and #x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))# #(color(red)(a^2) xx color(purple)(a))/(color(blue)(b^3) xx color(green)(b^5)) = (color(red)(a^2) xx color(purple)(a^1))/(color(blue)(b^3) xx color(green)(b^5)) = a^(color(red)(2) + color(purple)(1))/b^(color(blue)(3) + color(green)(5)) = a^3/b^8#

Avery Alexander · Answer

undefined To simplify the expression (a^2/b^3)/(b^5/a), we can multiply the numerator and denominator by the reciprocal of the denominator. This gives us (a^2/b^3) * (a/b^5). Simplifying further, we combine the like terms in the numerator and denominator, resulting in a^3/b^8. Therefore, the simplified expression is a^3/b^8.